Question

7. If (x - 1) is a factor of x4 – 3x3 + bx2 + 8x - 4, then find the value of b.
8. Show that the factors of x + x - 12 are x - 3 and x + 4.
2​

Answer 1

$\huge\sf\underline\green{Solution}$

7) (x - 1 ) is a factor So, x = 1

Lets substuite

x⁴ - 3x³ + bx² + 8x -4 =0

(1)⁴ - 3 (1)³ + b(1)² + 8(1) -4=0

1 - 3 + b + 8 -4 =0

9-7 + b =0

2 + b =0

b = -2

$\huge\sf\underline\pink{Solution}$

$\huge\sf\underline\red{Correct question}$

We have to prove x-3 and x+4 is a factor of x²+x-12=0

$\huge\sf\underline{Case- 1 }$

x - 3 =0

x=3 Substuite

(3)²+3-12 =0

9+3-12=0

12-12=0

0=0 Hence Case 1 proved

$\huge\sf\underline{Case -2}$

x+4=0

x= -4 Lets substuite

(-4)²-4-12=0

16-16=0

0=0

Hence we can say that (x-3)(x+4) are factors of x²+3x-12

Hence both are completed!!!